Conventionally, there has been provided a pump unit shown in FIG. 4. This pump unit has a fixed-capacity type pump 52 whose rotational speed is variably driven by a variable-speed motor 51, and a controller 53 for controlling the rotational speed of the variable-speed motor 51 by changing the frequency of supply current to the motor 51. This controller 53, upon receiving a signal from a pressure sensor 54 which detects a pressure of a discharge line of the pump 52, controls the rotational speed of the variable-speed motor 51 so that the value of the pressure detected by the pressure sensor 54 becomes a specified value, thus controlling the rotational speed of the pump 52.
However, in this conventional pump unit, since one fixed-capacity type pump 52 is driven by the variable-speed motor 51, a large-torque motor or a small- and fixed-capacity type pump needs to be used in order to obtain a high pressure as the discharge pressure of the fixed-capacity type pump 52. Using the large-torque motor would cause a problem of an upsizing of the pump unit as well as an increase in cost. Also, using the small- and fixed-capacity type pump would cause the rotational speeds of the pump and the motor to become excessively large ones during high flow-rate operations, posing a problem of excessively large noise and vibrations of the pump unit.